The Study On Max-min Optimization Problem For Semi-infinite Programming

Semi-infinite max-min optimization problem has been a popular hotspot of optimization theory in recent years.It has wide applications in many practical fields, Such as engineering technique,optimal control,economic equilibrium,information technology and computer network.The main four works is illustrated as follows:First,we introduce research of the problem and defect of research.Second,we presents an efficient element updating Newton-like algorithm for the semi-infinite minmax problems The basic way is to use element updating Newton-like algorithm to solve for a series approximate problems of semi-infinite minmax problems.There are three parts,introductions,bascl knowledge,and element up dating Newton-like algorithm.The convergence of method is discussed and the method is beyond linear convergence.Third,we present an approach for generalized semi-infinite minmax problems. We use the augmented Lagrangian function to remove the constraintsf(x,y)≤0, then use element updating Newton-like algorithm to solve the fainting problem.The convergence of method is discussed.Finally,numerical results demonstrate that the algorithm is efficient.